Question

1) The angular velocity of a wheel is 70 rad/sec. If the radius of the wheel is 0.5 m, then linear velocity of the wheel is:
{answer should come 35 m/s}

2) The angular displacement of the minute hand of a clock in 20 minutes is:
{answer should come $\frac{2\pi}{3}$ radian}

3) If the frequency of a particle performing circular motion increases from 60 rpm to 180 rpm in 20 seconds, its angular acceleration is :
{answer should come 0.6284$rad/s^{2}$ }

4) A flywheel rotates at a constant speed of 2400 rpm. The angle described by the shaft in radian in one second is :
{answer should come 80 $\pi$}

Answer 1

1. Angular velocity ω = 70 rad /sec 
      Rotations per second = n = ω / 2π  = 35/π per sec
      linear velocity = distance covered in one rotation * n 
                             = 2 π 0.5 * 35 / π = 35 m/sec

2. Angular displacement of minutes hand in 20 minutes 
              = total angle moved in one hour * 20 minutes / 60 minutes 
              = 2 π * 20 / 60 = 2 π /3        
       Minutes hand circles completely in 60 minutes. so angle covered = 2π

3.  ω = rpm * 2π / 60 radians/sec
        ω2 - ω1 = 180 - 60 = 120 rpm = 120 * 2π / 60 = 4 π rad/sec
        Angular acceleration = α = (ω2 - ω1) / time = 4π/20 = 0.6283 rad/sec²

4.  angle described in one second = ω * 1sec = rpm * (2π / 60) * 1 sec 
                            = 2400 * 2π/60 = 80 π radians